Adaptive Tracking Control for Unknown Dynamics Systems with SINDYc-based Sparse Identi¯cation

Machine learning-based data-driven approaches have greatly improved system identi¯cation capabilities and facilitated the application of model-based control algorithms. However, techniques such as neural networks require signi¯cant amounts of training data and have limited generalization capabilities. To overcome this problem, we employ the sparse identi¯cation of nonlinear dynamics with control (SINDYc) for system identi¯cation, which considers both system states and control inputs. Based on the identi¯ed system, we design the controller using the backstepping control method. In order to make the algorithm more practical in real-world scenarios, we introduce an input saturation compensation system into the controller design. Additionally, we apply a command ¯lter into the method to avoid deriving a virtual control signal and reduce the computational complexity of the controller. Through stability analysis, the proposed control algorithm ensures that the tracking error in the system is bounded. Finally, we verify the e®ectiveness of the proposed SINDYc-Backstepping framework by conducting simulations using a single-link robot arm.